Pub Date : 2020-06-30DOI: 10.22034/JSM.2019.1870709.1457
H. Salehipour, M. Jamshidi, A. Shahsavar
In this research static deflection and free vibration of homogeneous nanobeams coated by a functionally graded (FG) layer is investigated according to the nonlocal elasticity theory. A higher order beam theory is used that does not need the shear correction factor. The equations of motion (equilibrium equations) are extracted by using Hamilton’s principle. The material properties are considered to vary in the thickness direction of FG coated layer. This nonlocal nanobeam model incorporates the length scale parameter (nonlocal parameter) that can capture the small scale effects. In the numerical results section, the effects of different parameters, especially the ratio of thickness of FG layer to the total thickness of the beam are considered and discussed. The results reveal that the frequency is maximum for a special value of material power index. Also, increasing the ratio of thickness of FG layer to the total thickness of the beam increases the static deflection and decreases the natural frequencies. These results help with the understanding such coated structures and designing them carefully. The results also show that the new nonlocal FG nanobeam model produces larger vibration and smaller deflection than homogeneous nonlocal nanobeam.
{"title":"Considering Bending and Vibration of Homogeneous Nanobeam Coated by a FG Layer","authors":"H. Salehipour, M. Jamshidi, A. Shahsavar","doi":"10.22034/JSM.2019.1870709.1457","DOIUrl":"https://doi.org/10.22034/JSM.2019.1870709.1457","url":null,"abstract":"In this research static deflection and free vibration of homogeneous nanobeams coated by a functionally graded (FG) layer is investigated according to the nonlocal elasticity theory. A higher order beam theory is used that does not need the shear correction factor. The equations of motion (equilibrium equations) are extracted by using Hamilton’s principle. The material properties are considered to vary in the thickness direction of FG coated layer. This nonlocal nanobeam model incorporates the length scale parameter (nonlocal parameter) that can capture the small scale effects. In the numerical results section, the effects of different parameters, especially the ratio of thickness of FG layer to the total thickness of the beam are considered and discussed. The results reveal that the frequency is maximum for a special value of material power index. Also, increasing the ratio of thickness of FG layer to the total thickness of the beam increases the static deflection and decreases the natural frequencies. These results help with the understanding such coated structures and designing them carefully. The results also show that the new nonlocal FG nanobeam model produces larger vibration and smaller deflection than homogeneous nonlocal nanobeam.","PeriodicalId":17126,"journal":{"name":"Journal of Solid Mechanics and Materials Engineering","volume":"32 1","pages":"411-437"},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82183533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-30DOI: 10.22034/JSM.2019.1871279.1459
R. Bagheri, M. .. Monfared
In this paper, the analytical solution of an electric and Volterra edge dislocation in a functionally graded piezoelectric (FGP) medium is obtained by means of complex Fourier transform. The system is subjected to in-plane mechanical and electrical loading. The material properties of the medium vary exponentially with coordinating parallel to the crack. In this study, the rate of the gradual change of the shear moduli and mass density is assumed to be same. At first, the Volterra edge dislocation solutions are employed to derive singular integral equations in the form of Cauchy singularity for an FGP plane containing multiple horizontal moving cracks. Then, these equations are solved numerically to obtain dislocation density functions on moving crack surfaces. Finally, the effects of the crack moving velocity, material properties, electromechanical coupling factor and cracks arrangement on the normalized mode I and mode II stress intensity factors and electric displacement intensity factor are studied.
{"title":"In-Plane Analysis of an FGP Plane Weakened by Multiple Moving Cracks","authors":"R. Bagheri, M. .. Monfared","doi":"10.22034/JSM.2019.1871279.1459","DOIUrl":"https://doi.org/10.22034/JSM.2019.1871279.1459","url":null,"abstract":"In this paper, the analytical solution of an electric and Volterra edge dislocation in a functionally graded piezoelectric (FGP) medium is obtained by means of complex Fourier transform. The system is subjected to in-plane mechanical and electrical loading. The material properties of the medium vary exponentially with coordinating parallel to the crack. In this study, the rate of the gradual change of the shear moduli and mass density is assumed to be same. At first, the Volterra edge dislocation solutions are employed to derive singular integral equations in the form of Cauchy singularity for an FGP plane containing multiple horizontal moving cracks. Then, these equations are solved numerically to obtain dislocation density functions on moving crack surfaces. Finally, the effects of the crack moving velocity, material properties, electromechanical coupling factor and cracks arrangement on the normalized mode I and mode II stress intensity factors and electric displacement intensity factor are studied.","PeriodicalId":17126,"journal":{"name":"Journal of Solid Mechanics and Materials Engineering","volume":"6 1","pages":"438-454"},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87517364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-30DOI: 10.22034/JSM.2019.1867884.1437
H. Ziou, M. Himeur, H. Guenfoud, M. Guenfoud
Finite element formulations based generally on classical beam theories such as Euler-Bernoulli or Timoshenko. Sometimes, these two formulations could be problematic expressed in terms of restrictions of Euler-Bernoulli beam theory, in case of thicker beams due to non-consideration of transverse shear; phenomenon that is known as shear locking characterized the Timoshenko beam theory, in case of thin beams; problem of slow of convergence in regards to the element of Timoshenko beam. In responding to this problematic, a new beam finite element model is developed to study the static bending of functionally graded beams. The originality of this model lies in the use of a deformation approach with the consideration of a central node positioned in the middle of the beam. The degrees of freedom of this node are subsequently eliminated by the method of static condensation. In addition, this model is suitable for all linear structures regardless of L/h ratio. Functionally graded material beams have a smooth variation of material properties due to continuous change in micro structural details. The mechanical properties of the beam are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. A simply supported beam subjected to uniform load for different length-to-thickness ratio has been chosen in the analysis. Finite element solutions obtained with the new finite element model are presented, and the obtained results are evaluated with the existing solutions to verify the validity of the present model.
{"title":"An Efficient Finite Element Formulation Based on Deformation Approach for Bending of Functionally Graded Beams","authors":"H. Ziou, M. Himeur, H. Guenfoud, M. Guenfoud","doi":"10.22034/JSM.2019.1867884.1437","DOIUrl":"https://doi.org/10.22034/JSM.2019.1867884.1437","url":null,"abstract":"Finite element formulations based generally on classical beam theories such as Euler-Bernoulli or Timoshenko. Sometimes, these two formulations could be problematic expressed in terms of restrictions of Euler-Bernoulli beam theory, in case of thicker beams due to non-consideration of transverse shear; phenomenon that is known as shear locking characterized the Timoshenko beam theory, in case of thin beams; problem of slow of convergence in regards to the element of Timoshenko beam. In responding to this problematic, a new beam finite element model is developed to study the static bending of functionally graded beams. The originality of this model lies in the use of a deformation approach with the consideration of a central node positioned in the middle of the beam. The degrees of freedom of this node are subsequently eliminated by the method of static condensation. In addition, this model is suitable for all linear structures regardless of L/h ratio. Functionally graded material beams have a smooth variation of material properties due to continuous change in micro structural details. The mechanical properties of the beam are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. A simply supported beam subjected to uniform load for different length-to-thickness ratio has been chosen in the analysis. Finite element solutions obtained with the new finite element model are presented, and the obtained results are evaluated with the existing solutions to verify the validity of the present model.","PeriodicalId":17126,"journal":{"name":"Journal of Solid Mechanics and Materials Engineering","volume":"14 1","pages":"343-357"},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86456648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-30DOI: 10.22034/JSM.2019.1876608.1482
R. N. Bouharkat, A. Sahli, S. Sahli
Given any structure, we seek to find the solution of mechanical problem as precisely and efficiently as possible. Within this condition, the BEM is robust and promising development, standing out in the analysis of cases with occurrence of large stress gradients, as in problems of fracture mechanics. Moreover, in BEM the modeling of infinite means is performed naturally, without the use of approximations. For methods involving domain integration, such as FEM, this is not possible, as models with high number of elements are usually adopted and their ends are considered flexible supports. This paper deals with the development of numerical models based on the BEM for mechanical analysis of stiffened domains. In the modeling of hardeners, immersed in a medium defined by the BEM, we tried to use both the FEM, already present in the literature, and the BEM 1D, being a new formulation. The objective was to perform the coupling of BEM with FEM and BEM 1D for elements of any degree of approximation, evaluating both isotropic and anisotropic medium. In addition, a complementary objective was to verify the effects of the adoption of different discretization and approximation degrees on the stiffeners. However, the coupling with the BEM 1D leaded to more stable results and better approximations. It was observed that the FEM results were instable for many results, mainly in the quadratic approximations. When the approximation degree rises, the methods tend to converge to equivalent results, becoming very close in fourth degree approximation. Lastly, it was observed stress concentration in the stiffeners ends. In these regions, the discretization and the approximation degree have large influence to the numerical response.
{"title":"Stiffeners Mechanical Effect Analysis by Numerical Coupling","authors":"R. N. Bouharkat, A. Sahli, S. Sahli","doi":"10.22034/JSM.2019.1876608.1482","DOIUrl":"https://doi.org/10.22034/JSM.2019.1876608.1482","url":null,"abstract":"Given any structure, we seek to find the solution of mechanical problem as precisely and efficiently as possible. Within this condition, the BEM is robust and promising development, standing out in the analysis of cases with occurrence of large stress gradients, as in problems of fracture mechanics. Moreover, in BEM the modeling of infinite means is performed naturally, without the use of approximations. For methods involving domain integration, such as FEM, this is not possible, as models with high number of elements are usually adopted and their ends are considered flexible supports. This paper deals with the development of numerical models based on the BEM for mechanical analysis of stiffened domains. In the modeling of hardeners, immersed in a medium defined by the BEM, we tried to use both the FEM, already present in the literature, and the BEM 1D, being a new formulation. The objective was to perform the coupling of BEM with FEM and BEM 1D for elements of any degree of approximation, evaluating both isotropic and anisotropic medium. In addition, a complementary objective was to verify the effects of the adoption of different discretization and approximation degrees on the stiffeners. However, the coupling with the BEM 1D leaded to more stable results and better approximations. It was observed that the FEM results were instable for many results, mainly in the quadratic approximations. When the approximation degree rises, the methods tend to converge to equivalent results, becoming very close in fourth degree approximation. Lastly, it was observed stress concentration in the stiffeners ends. In these regions, the discretization and the approximation degree have large influence to the numerical response.","PeriodicalId":17126,"journal":{"name":"Journal of Solid Mechanics and Materials Engineering","volume":"44 1","pages":"476-492"},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83767587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-30DOI: 10.22034/JSM.2019.1873720.1466
N. Ahlawat, R. Lal
An analysis has been presented of the effect of elastic foundation and uniform in-plane peripheral loading on the natural frequencies and mode shapes of circular plates of varying thickness exhibiting bi-directional functionally graded characteristics, on the basis of first order shear deformation theory. The material properties of the plate are varying following a power-law in both the radial and transverse directions. The numerical solutions of the coupled differential equations leading the motion of simply supported and clamped plates acquired by using Hamilton’s principle, is attained by harmonic differential quadrature method. The effect of different plate parameters namely gradient index, heterogeneity parameter, density parameter, taper parameter and thickness parameter is illustrated on the vibration characteristics for the first three modes of vibration for various values of in-plane peripheral loading parameter together with foundation parameter. Critical buckling loads in compression are calculated for both the boundary conditions by putting the frequencies to zero. The reliability of the present technique is confirmed by comparing the results with exact values and results of published work.
{"title":"Effect of Winkler Foundation on Radially Symmetric Vibrations of Bi-Directional FGM Non-Uniform Mindlin’s Circular Plate Subjected to In-Plane Peripheral Loading","authors":"N. Ahlawat, R. Lal","doi":"10.22034/JSM.2019.1873720.1466","DOIUrl":"https://doi.org/10.22034/JSM.2019.1873720.1466","url":null,"abstract":"An analysis has been presented of the effect of elastic foundation and uniform in-plane peripheral loading on the natural frequencies and mode shapes of circular plates of varying thickness exhibiting bi-directional functionally graded characteristics, on the basis of first order shear deformation theory. The material properties of the plate are varying following a power-law in both the radial and transverse directions. The numerical solutions of the coupled differential equations leading the motion of simply supported and clamped plates acquired by using Hamilton’s principle, is attained by harmonic differential quadrature method. The effect of different plate parameters namely gradient index, heterogeneity parameter, density parameter, taper parameter and thickness parameter is illustrated on the vibration characteristics for the first three modes of vibration for various values of in-plane peripheral loading parameter together with foundation parameter. Critical buckling loads in compression are calculated for both the boundary conditions by putting the frequencies to zero. The reliability of the present technique is confirmed by comparing the results with exact values and results of published work.","PeriodicalId":17126,"journal":{"name":"Journal of Solid Mechanics and Materials Engineering","volume":"37 1","pages":"455-475"},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85601333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-30DOI: 10.22034/JSM.2019.1869981.1450
M. Molla-Alipour, M. Shariyat, M. Shaban
In the present research, a unified formulation for free vibration analysis of the bidirectional functionally graded conical and cylindrical shells and annular plates on elastic foundations is developed. To cover more individual cases and optimally tailored material properties, the material properties are assumed to vary in both the meridian/radial and transverse directions. The shell/plate is assumed to be supported by a non-uniform Winkler-type elastic foundation in addition to the edge constraints. Therefore, the considered problem contains some complexities that have not been considered together in the available researches. The proposed unified formulation is derived based on the principle of minimum total potential energy and solved using a differential transform analytical method whose center is located at the outer edge of the shell or plate; so that the resulting semi-analytical solution can be employed not only for truncated conical shells and annular plates, but also for complete conical shells and circular plates. Accuracy of results of the proposed unified formulation is verified by comparing the results with those of the three-dimensional theory of elasticity extracted from the ABAQUS finite element analysis code. A variety of the edge condition combinations are considered in the results section. A comprehensive parametric study including assessment of influences of the material properties indices, thickness to radius ratio, stiffness distribution of the elastic foundation, and various boundary conditions, is accomplished. Results reveal that influence of the meridian variations of the material properties on the natural frequencies is more remarkable than that of the transverse gradation.
{"title":"Free Vibration Analysis of Bidirectional Functionally Graded Conical/Cylindrical Shells and Annular Plates on Nonlinear Elastic Foundations, Based on a Unified Differential Transform Analytical Formulation","authors":"M. Molla-Alipour, M. Shariyat, M. Shaban","doi":"10.22034/JSM.2019.1869981.1450","DOIUrl":"https://doi.org/10.22034/JSM.2019.1869981.1450","url":null,"abstract":"In the present research, a unified formulation for free vibration analysis of the bidirectional functionally graded conical and cylindrical shells and annular plates on elastic foundations is developed. To cover more individual cases and optimally tailored material properties, the material properties are assumed to vary in both the meridian/radial and transverse directions. The shell/plate is assumed to be supported by a non-uniform Winkler-type elastic foundation in addition to the edge constraints. Therefore, the considered problem contains some complexities that have not been considered together in the available researches. The proposed unified formulation is derived based on the principle of minimum total potential energy and solved using a differential transform analytical method whose center is located at the outer edge of the shell or plate; so that the resulting semi-analytical solution can be employed not only for truncated conical shells and annular plates, but also for complete conical shells and circular plates. Accuracy of results of the proposed unified formulation is verified by comparing the results with those of the three-dimensional theory of elasticity extracted from the ABAQUS finite element analysis code. A variety of the edge condition combinations are considered in the results section. A comprehensive parametric study including assessment of influences of the material properties indices, thickness to radius ratio, stiffness distribution of the elastic foundation, and various boundary conditions, is accomplished. Results reveal that influence of the meridian variations of the material properties on the natural frequencies is more remarkable than that of the transverse gradation.","PeriodicalId":17126,"journal":{"name":"Journal of Solid Mechanics and Materials Engineering","volume":"77 1","pages":"385-400"},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81161759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-30DOI: 10.22034/JSM.2019.1866762.1428
A. Hassani, A. Hassani
In this article, the anti-plane deformation of an orthotropic sector with multiple defects is studied analytically. The solution of a Volterra-type screw dislocation problem in a sector is first obtained by means of a finite Fourier cosine transform. The closed form solution is then derived for displacement and stress fields over the sector domain. Next, the distributed dislocation method is employed to obtain integral equations of the sector with cracks and cavities under anti-plane traction. These equations are of Cauchy singular kind, which are solved numerically by generalizing a numerical method available in the literature by means of expanding the continuous integrands of integral equations with different weight functions in terms of Chebyshoff and Jacobi polynomials. A set of examples are presented to demonstrate the applicability of the proposed solution procedure. The geometric and force singularities of stress fields in the sector are also studied and compared to the earlier reports in the literature.
{"title":"Analytical Stress Solutions of an Orthotropic Sector Weakened by Multiple Defects by Dislocation Approach","authors":"A. Hassani, A. Hassani","doi":"10.22034/JSM.2019.1866762.1428","DOIUrl":"https://doi.org/10.22034/JSM.2019.1866762.1428","url":null,"abstract":"In this article, the anti-plane deformation of an orthotropic sector with multiple defects is studied analytically. The solution of a Volterra-type screw dislocation problem in a sector is first obtained by means of a finite Fourier cosine transform. The closed form solution is then derived for displacement and stress fields over the sector domain. Next, the distributed dislocation method is employed to obtain integral equations of the sector with cracks and cavities under anti-plane traction. These equations are of Cauchy singular kind, which are solved numerically by generalizing a numerical method available in the literature by means of expanding the continuous integrands of integral equations with different weight functions in terms of Chebyshoff and Jacobi polynomials. A set of examples are presented to demonstrate the applicability of the proposed solution procedure. The geometric and force singularities of stress fields in the sector are also studied and compared to the earlier reports in the literature.","PeriodicalId":17126,"journal":{"name":"Journal of Solid Mechanics and Materials Engineering","volume":"1 1","pages":"366-384"},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82360506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-30DOI: 10.22034/JSM.2020.672978
N. Haghshenas, A. G. Arani, A. Javanbakht, M. Karimi
In this investigation a suitable algorithm for the detection of cracks in the pressure vessels is presented. The equations of motion for the vessel are obtained and transferred into the wavelet space in a simplified form resulted from time and position approximations. The locations of cracks are randomly distributed in different regions of the structure to cover the whole geometry of the pressure vessel. Furthermore, the pressure vessel is installed vertically with a fixed end at the bottom of each of its four leg supports. Then, the results are transferred to the wavelet space using Daubechies wavelet families. From the comparison of the displacement results associated with the intact and damaged vessels, it can be clearly seen that the crack location can be accurately detected noting the alteration in the wavelet output diagrams .The results of the crack detection show that with the proper selection of the wavelet type, the wavelet based finite element method is a suitable and nondestructive method as well as a powerful numerical tool for the detection of cracks and other discontinuities in the pressure vessels. The results of this investigation can be used in the marine and aerospace industries as well as power stations.
{"title":"A Novel Finite-Element-Based Algorithm for Damage Detection in the Pressure Vessels Using the Wavelet Approach","authors":"N. Haghshenas, A. G. Arani, A. Javanbakht, M. Karimi","doi":"10.22034/JSM.2020.672978","DOIUrl":"https://doi.org/10.22034/JSM.2020.672978","url":null,"abstract":"In this investigation a suitable algorithm for the detection of cracks in the pressure vessels is presented. The equations of motion for the vessel are obtained and transferred into the wavelet space in a simplified form resulted from time and position approximations. The locations of cracks are randomly distributed in different regions of the structure to cover the whole geometry of the pressure vessel. Furthermore, the pressure vessel is installed vertically with a fixed end at the bottom of each of its four leg supports. Then, the results are transferred to the wavelet space using Daubechies wavelet families. From the comparison of the displacement results associated with the intact and damaged vessels, it can be clearly seen that the crack location can be accurately detected noting the alteration in the wavelet output diagrams .The results of the crack detection show that with the proper selection of the wavelet type, the wavelet based finite element method is a suitable and nondestructive method as well as a powerful numerical tool for the detection of cracks and other discontinuities in the pressure vessels. The results of this investigation can be used in the marine and aerospace industries as well as power stations.","PeriodicalId":17126,"journal":{"name":"Journal of Solid Mechanics and Materials Engineering","volume":"8 1","pages":"249-262"},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83387595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-30DOI: 10.22034/JSM.2019.563701.1261
K. Paul, B. Mukhopadhyay
A generalized thermo-elastic diffusion problem in a functionally graded isotropic, unbounded, rotating elastic medium due to a periodically varying heat source in the context of fractional order theory is considered in our present work. The governing equations of the theory for a functionally graded material with GNIII model are established. Analytical solution of the problem is derived in Laplace-Fourier transform domain. Finally, numerical inversions are used to show the effect of rotation, non-homogeneity and fractional parameter on stresses, displacement, chemical potential, mass distribution, temperature, etc. and those are illustrated graphically.
{"title":"A Generalized Thermo-Elastic Diffusion Problem in a Functionally Graded Rotating Media Using Fractional Order Theory","authors":"K. Paul, B. Mukhopadhyay","doi":"10.22034/JSM.2019.563701.1261","DOIUrl":"https://doi.org/10.22034/JSM.2019.563701.1261","url":null,"abstract":"A generalized thermo-elastic diffusion problem in a functionally graded isotropic, unbounded, rotating elastic medium due to a periodically varying heat source in the context of fractional order theory is considered in our present work. The governing equations of the theory for a functionally graded material with GNIII model are established. Analytical solution of the problem is derived in Laplace-Fourier transform domain. Finally, numerical inversions are used to show the effect of rotation, non-homogeneity and fractional parameter on stresses, displacement, chemical potential, mass distribution, temperature, etc. and those are illustrated graphically.","PeriodicalId":17126,"journal":{"name":"Journal of Solid Mechanics and Materials Engineering","volume":"22 1","pages":"263-277"},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74731091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-30DOI: 10.22034/JSM.2019.1870009.1451
T. Akano, O. Fakinlede, P. Olayiwola
In cylindrical continua, hoop stresses are induced due to the circumferential failure. This mainly happens when the cylinder is subjected to mechanical loads which vary in the circumferential directions. On the other hand, radial stress is stress in the direction of or opposite to the central axis of a cylindrical body. In the present study, the influence of curvilinear anisotropy on the radial and tangential stresses of the polar-orthotropic hollow cylinder is presented. The governing equations were derived to evaluate the radial and hoop stresses inside the material. A semi-analytical method through differential transform method (DTM) for the polar-orthotropic hollow cylinder is implemented in the solution. The findings, based on polar-orthotropy, of the effect of the radial and circumferential loads on the radial and hoop stresses of the growing cylinders, show elastic responses that assist in identifying some of the outstanding properties of the curvilinear anisotropic continuums. It is also revealed that the characteristic response of various wall thicknesses of the cylindrical segment is influenced by the fibre orientation, radial and tangential stresses. This work has shown that the curvilinear anisotropy momentously affects the radial and hoop stresses on the polar-orthotropic hollow cylinder.
{"title":"On Analysis of Stress Concentration in Curvilinear Anisotropic Deformable Continuum Bodies","authors":"T. Akano, O. Fakinlede, P. Olayiwola","doi":"10.22034/JSM.2019.1870009.1451","DOIUrl":"https://doi.org/10.22034/JSM.2019.1870009.1451","url":null,"abstract":"In cylindrical continua, hoop stresses are induced due to the circumferential failure. This mainly happens when the cylinder is subjected to mechanical loads which vary in the circumferential directions. On the other hand, radial stress is stress in the direction of or opposite to the central axis of a cylindrical body. In the present study, the influence of curvilinear anisotropy on the radial and tangential stresses of the polar-orthotropic hollow cylinder is presented. The governing equations were derived to evaluate the radial and hoop stresses inside the material. A semi-analytical method through differential transform method (DTM) for the polar-orthotropic hollow cylinder is implemented in the solution. The findings, based on polar-orthotropy, of the effect of the radial and circumferential loads on the radial and hoop stresses of the growing cylinders, show elastic responses that assist in identifying some of the outstanding properties of the curvilinear anisotropic continuums. It is also revealed that the characteristic response of various wall thicknesses of the cylindrical segment is influenced by the fibre orientation, radial and tangential stresses. This work has shown that the curvilinear anisotropy momentously affects the radial and hoop stresses on the polar-orthotropic hollow cylinder.","PeriodicalId":17126,"journal":{"name":"Journal of Solid Mechanics and Materials Engineering","volume":"36 1","pages":"401-410"},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82232079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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